Lady Warsi said on Monday she would co-operate with any inquiry, but declined to answer questions over whether she would resign over the row.

Speaking to ITV News during a visit to Malaysia, she said: "I take these allegations very seriously; it's why I said right at the outset that I would fully co-operate with any investigation. I believe that being a member of the House of Lords is a privilege. I take that privilege seriously.

"It's why I have always insured that my conduct including in relation to expenses and allowances is both in accordance with the law and the spirit of the rules."

Downing Street has so far made no show of support for the peer. Tory deputy chairman Michael Fallon said only that Lady Warsi "believes" she acted within the rules, but he admitted that the controversy was embarrassing for the party.

Lady Warsi insisted she made an "appropriate payment" to her friend - Tory official Naweed Khan, who is now one of her aides - for the nights she stayed at the property in Acton, west London.

Mr Khan supported her assertion, releasing a statement saying she made a payment each time she stayed.

The peer, now a Cabinet Office minister, was claiming Lords subsistence of £165.50 a night at the time in 2008 to which the allegations relate.

Earlier the former sleaze watchdog Sir Alistair Graham suggested that Lady Warsi should relinquish her ministerial office until any inquiries were complete.

The ex-chairman of the Committee on Standards in Public Life, said: "At the moment it all looks very muddy and blurred.

"I personally am always of the view, when ministers face very serious allegations that seem to have some strength to them, then it's better that they stand down from their ministerial post while that investigation takes place, but of course that is a matter for the Prime Minister."

Mr Mann said he would be writing to the Lords standards commissioner requesting an investigation. "If you are paying no rent where you are staying, you can't possibly be claiming subsistence for staying there," he said.

Liberal Democrat backbencher Bob Russell suggested that the matter should be investigated by the police. "I think there's a prima facie case for this to be looked at by the police," he said.

In a further embarrassment for Lady Warsi, the most senior Muslim politician in Britain, she was forced to admit failing to declare rental income on a London flat in the Lords register of interests.

She said the omission was due to an "oversight", adding that she had reported the letting of her Wembley flat in the Register of Ministers' Interests. The arrangement had also been declared to the Cabinet Office and HM Revenue and Customs, she said.

The peer bought the property in 2007 but moved closer to Parliament when she became a minister in 2010, after which she began letting the Wembley flat.

In a statement last night, Lady Warsi said she contracted to buy the flat in September 2007, but it was not due to be ready until the following year.

In the interim she stayed predominantly at two hotels but also, for "occasional nights", at an Acton property occupied by Mr Khan.

"For the nights that I stayed as a guest of Naweed Khan, I made an appropriate financial payment equivalent to what I was paying at the time in hotel costs," she said.

"In March 2008, I moved into the flat in Wembley. As I was living in the property, it was therefore not registrable on the Register of Lords' Interests."

Conservative deputy chairman Michael Fallon said: "These sorts of thing are always embarrassing but the key thing here is that Lady Warsi has admitted she's made a mistake, she's apologised for it.

"She's corrected the record now and she's very happy to cooperate with any investigation back into her claims and I think it should be left at that until any investigation is reported."

A Conservative Party spokeswoman later said Lady Warsi had referred herself to the Standards Commissioner, asking him to investigate her expenses claims.